QFactory: classically-instructed remote secret qubits preparation

TL;DR

This paper introduces a secure protocol for classically instructing a quantum server to prepare random secret qubits, based on trapdoor functions and the Learning With Errors problem, with extensions for larger state sets and verifiability.

Contribution

It presents a simplified primitive using BB84 states, a secure protocol against malicious servers, and new extensions including verifiability and larger state sets.

Findings

Protocol is secure against arbitrary malicious servers.

Security is based on the hardness of Learning With Errors.

Introduces blind self-testing for verifiability.

Abstract

The functionality of classically-instructed remotely prepared random secret qubits was introduced in (Cojocaru et al 2018) as a way to enable classical parties to participate in secure quantum computation and communications protocols. The idea is that a classical party (client) instructs a quantum party (server) to generate a qubit to the server's side that is random, unknown to the server but known to the client. Such task is only possible under computational assumptions. In this contribution we define a simpler (basic) primitive consisting of only BB84 states, and give a protocol that realizes this primitive and that is secure against the strongest possible adversary (an arbitrarily deviating malicious server). The specific functions used, were constructed based on known trapdoor one-way functions, resulting to the security of our basic primitive being reduced to the hardness of the Learning With Errors problem. We then give a number of extensions, building on this basic module: extension to larger set of states (that includes non-Clifford states); proper consideration of the abort case; and verifiablity on the module level. The latter is based on "blind self-testing", a notion we introduced, proved in a limited setting and conjectured its validity for the most general case.